Disaster recovery plans are mandatory, and with that comes a good backup plan, and I'm sure in this case they had one.
The 2013 incident seems to have started with backup Plan A which was then ditched for Plan B which eventually included being sent an electronic backup copy from April by Frequentis in Vienna. It isn't clear whether this was the "good backup plan" that they had in place.
For the 2014 incident, I see the Observer today repeats this version of the story :
Finally, at the end of the year, there was
chaos at Nats, the public-private partnership that runs Britain’s air traffic control systems. The whole of London’s airspace was closed for more than an hour on 12 December, with disruption continuing for several subsequent days. Aircraft were stuck in holding patterns over Heathrow, or diverted to other airports, with hundreds of flights cancelled. Vince Cable said Nats had been “penny wise and pound foolish” and was running “ancient computer systems, which then crash”. It eventually emerged that a single line of computer code more than 25 years old was responsible for the shutdown.
Fear of flying: the spectre that haunts modern life | World news | The Guardian
Any word from the CAA on the 2014 inquiry chairman yet ?